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On complete moment convergence for weighted sums of negatively superadditive dependent random variables

Haiwu Huang, Xuewen Lu (2020)

Applications of Mathematics

In this work, the complete moment convergence and complete convergence for weighted sums of negatively superadditive dependent (NSD) random variables are studied, and some equivalent conditions of these strong convergences are established. These main results generalize and improve the corresponding theorems of Baum and Katz (1965) and Chow (1988) to weighted sums of NSD random variables without the assumption of identical distribution. As an application, a Marcinkiewicz-Zygmund-type strong law of...

On entropies for random partitions of the unit segment

Milena Bieniek, Dominik Szynal (2008)

Kybernetika

We prove the complete convergence of Shannon’s, paired, genetic and α-entropy for random partitions of the unit segment. We also derive exact expressions for expectations and variances of the above entropies using special functions.

On fully coupled continuous time random walks

W. Szczotka, P. Żebrowski (2012)

Applicationes Mathematicae

Continuous time random walks with jump sizes equal to the corresponding waiting times for jumps are considered. Sufficient conditions for the weak convergence of such processes are established and the limiting processes are identified. Furthermore one-dimensional distributions of the limiting processes are given under an additional assumption.

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